Helen, I too am in the UK and what I have said is based on what I did when I installed my Epson XP-710 about a months ago.
When you go to the URL I provided, make sure that you have selectd the right operating system (Mac) in the liitle box at the top right hand corner of the second page. In this page, three steps are described. Step 2 includes "Choose a Connection Method" - select "WIFI or Ethernet" and then click on "Download". This should download the file EpsonNet Setup_WW_371_31.dmg. Double click on this. Quite honestly, I can't remember what it does and it may simply repeat something you have already done, but it may also be a key stage in the setup process. Then, in Step 3', click on the "Epson.com" icon at the bottom left of the page and follow the steps to get to the UK site where there will be a page of small pictures, with one of these called "Support". Open this and where it says "Enter in your model"', do NOT do this but click in the "Click Here" link and subsequently enter in your product details (All-in-one, XP-710, Mac Intel). You should then find a page listing all the available downloads. You have already obtained epson37757EU.dmg and this lead you to the Epson Scan Installer. Were you able to double click on this?
You say that you can scan - are you using the utility that looks like Image Capture and what sort of results do you get?